100 citations · 328 across the 12 of their papers we have counts for
13 papers · 1 filter
Computability of a Whitney Extension
Andrea Brun, Guido Gherardi, Alberto Marcone
We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if is a closed set represented s…
Completion of Choice
Vasco Brattka, Guido Gherardi
We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal role in Weihrauch complexity. For one, they can be used as landma…
Weihrauch goes Brouwerian
Vasco Brattka, Guido Gherardi
We prove that the Weihrauch lattice can be transformed into a Brouwer algebra by the consecutive application of two closure operators in the appropriate order: first completion and…
Interpolation in extensions of first-order logic
Guido Gherardi, Paolo Maffezioli, Eugenio Orlandelli
We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular…
Projection operators in the Weihrauch lattice
Guido Gherardi, Alberto Marcone, Arno Pauly
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice c…
The basis of Boole's logical calculus
Giovanna Corsi, Guido Gherardi
In the present paper we aim to provide a thoughtful and exegetical account of the fundamental ideas at the basis of Boole's theory, with the goal of developing our investigation st…
Weihrauch Complexity in Computable Analysis
Vasco Brattka, Guido Gherardi, Arno Pauly
We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussi…
The Vitali Covering Theorem in the Weihrauch Lattice
Vasco Brattka, Guido Gherardi, Rupert Hölzl +1
We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than…
Probabilistic Computability and Choice
Vasco Brattka, Guido Gherardi, Rupert Hölzl
We study the computational power of randomized computations on infinite objects, such as real numbers. In particular, we introduce the concept of a Las Vegas computable multi-value…
The Bolzano-Weierstrass Theorem is the Jump of Weak König's Lemma
Vasco Brattka, Guido Gherardi, Alberto Marcone
We classify the computational content of the Bolzano-Weierstrass Theorem and variants thereof in the Weihrauch lattice. For this purpose we first introduce the concept of a derivat…
Effective Choice and Boundedness Principles in Computable Analysis
Vasco Brattka, Guido Gherardi
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be contin…
Weihrauch Degrees, Omniscience Principles and Weak Computability
Vasco Brattka, Guido Gherardi
In this paper we study Weihrauch reducibility for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the…
How incomputable is the separable Hahn-Banach theorem?
Guido Gherardi, Alberto Marcone
We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis.…